基于校验矩阵优化扩展的码率兼容LDPC码设计

为了提高低密度校验（low density parity check, LDPC）码的打孔性能，提出一种基于校验矩阵优化扩展的码率兼容LDPC码设计方法。从码率兼容码的度分布约束关系出发，提出母码的度分布优化算法。在此基础上，结合打孔变量点的译码恢复规则，构造适合打孔的LDPC码校验矩阵。采用贪婪搜索算法逐级最大化不同类型的打孔变量点数目，提高码率兼容系列子码的误码性能。仿真结果表明，与编码高效的码率兼容LDPC码相比，所提方法生成的码率兼容子码误码性能有较大改善，特别是当码率大于0.8时，编码增益提高约0.7~0.8 dB。

Optimized extension of the parity check matrix for rate compatible LDPC codes

In order to improve the puncturing performance of low density parity check (LDPC) codes, a method to optimize the extension of the parity checking matrix for rate compatible LDPC codes is proposed. Considering the rate compatible constraint, an algorithm is presented to optimize the degree distribution of the LDPC codes. Based on the recovery rules of punctured nodes, a new structure of the parity check matrix is devised to facilitate puncturing. A greedy search algorithm is adopted to stepwisely maximize the number of diffe rent types of punctured variable nodes, which results in good puncturing performance. The experiment results show that the proposed method is superior to the efficiently encodable rate compatible LDPC (E2RC-LDPC) codes over wide range of rates. When the rate is greater than 0.8, the proposed method can obtain about 0.7~0.8 dB gain over the E2RC-LDPC codes.